During mission 4 the Hedoth structure is claimed by Neuropa and thus counts as an 'enemy structure' preventing you from gaining the eliminate enemy bonus after the mission. Do any of you have a suggestion to get around that?

Hello.
As You wrote, in order to gain the bonus, you have to wipe out enemy forces.
I may have some idea how to obtain it, but execution of my plan will be very time-consuming.
First and foremost, you have to fortify your south border from Mil-Agro raids. Then you should gather strong offensive party in order to destroy Neuropa Matter Converter (and entire base) near the Hedoth structure. If you do it, don't let surviving units appear near your Matter Converter, because it'll trigger script and end mission. Build second battlegroup in order to destroy Mil-Agro forces on the surface. If you are lucky and enemies haven't had build Matter Converters underground, you can force them both to surrender. After that, capture former Neuropa Hedoth Enhancer by one of your Drill Truck. In the end, gather survivors from Neuropa near your starting location. This'll end mission and luckily, may give you the bonus you want.
I hope that helps.

The Drill truck can take over the Hedoth Enhancer.

The main things I have found to be of strategical importance are:
-Get your starting income sorted ASAP!
-Get a good enough defense to hold your base on the surface.
-Have 1 hover vehicle on repair mode running after each melee combot (this makes them so much more durable as long as the hover vehicle lives of course x'D)
-Get control of the orbital and underground layers! (if you let the AI run free here - it will be a nightmare as it can and will produce units like crazy with the income gained from there!)
-Get your additional income from the orbital and underground layers going + increase your army production facilities (depending on what your prefer ;) )
-enjoy crushing your enemy! :D

I like to sit back in my base and send squadrons upon squadrons of jets to just wipe out my enemy :D so i go mass hangar!

My defense consists of
-2 or 3 melee combots (shield & katana or lasor sword; to increase the chances of an arm being cut off)
-4 or 5 ranged combots (missile legs & chest & 2 energy guns OR if I found & researched better, I will swap em ofcourse! :D)
-the gripping arm from neuropa is a nice addition for on defense to 'stun' enemies a bit while the rest of your combots/defenses hack/shoot into it!
-Mobile walls are great for in the campaign, just be wise on when to use them! (example: it is tempting to build up defenses 1st, then optimize income! however on hard difficulty this will make things very difficult! It is best to push for your starting economy ASAP! once that is sorted; build up your defense!

like with mission 4 for example:
-the 1st thing I do is start making a vehicle factory in orbit, THEN send my combots down to def my base. (make 5 hover vehicles here, and send them to different surfaces in orbit to build mobile walls to block the AI from them!
-2nd: send a hover vehicle down to the surface to make another vehicle factory
-make 5-6 hover vehicles for econ on the surface & make the 2 starting combots decent by swapping unwanted parts out with newly made/found parts
-make a drill truck +4 more hover vehicles to send down ASAP!
-put 2 of the underground hover vehicles on collecting lava/MJ, the other 2 make 4 vehicle factories & after it spam Cryofarms (if you hold down shift while building you can build in sequence!
ALSO: make more combot parts for defensive purposes
-make a few more hover vehicles underground for other lava patches if you find them, 2 more drill trucks & then spam tanks+ artillery

handy notes:
-holding down CTRL while clicking to produce something will make 5 of these per click!
-holding down shift allows you to give orders & build in sequence!
-you can make command groups by using CTRL+1 etc. (very helpful for swapping between layers fast!)
-command groups given during the build-up phase will NOT stay when you start the level! so don't bother yet :)
-recon poles: I suspect are underrated by many players: these are VERY useful on the missions where you have to wipe out all enemies for the bonus points! once you nearly completed the mission > send out several hover vehicles to build recon poles all over the map in sequence! (only needed on the surface layer > as the effect ripples through ALL layers!!!)
-an orbital surface that is being guarded by just 1 vehicle (that is not artillery!!!) can be taken over by a hover vehicle, by strategically building the mobile wall between it and the enemy! the wall will be damaged once completed, but it can be repaired faster as long as it is just 1 vehicle (if you don't like that kind of 'cheese-play' > send 2 hover vehicles and repair 1 with the other! ;D) - keep in mind: this trick requires you to build without being delayed, so you have to have/keep enough MJ in reserve!

Good luck, have fun & game on!